Dimension reduction aims to reduce the complexity of a regression without re-quiring a pre-specif... more Dimension reduction aims to reduce the complexity of a regression without re-quiring a pre-specified model. In the case of multivariate response regressions, covariance-based estimation methods for the k-th moment based dimension reduc-tion subspaces circumvent slicing and nonparametric estimation so that they are readily applicable to multivariate regression settings. In this article, the covariance-based method developed by Yin and Cook (2002) for univariate regressions is ex-tended to multivariate response regressions and a new method is proposed. Simu-lated and real data examples illustrating the theory are presented. Key Words: Central k-th moment subspace, Central mean subspaces,
Dimension reduction aims to reduce the complexity of a regression without re-quiring a pre-specif... more Dimension reduction aims to reduce the complexity of a regression without re-quiring a pre-specified model. In the case of multivariate response regressions, covariance-based estimation methods for the k-th moment based dimension reduc-tion subspaces circumvent slicing and nonparametric estimation so that they are readily applicable to multivariate regression settings. In this article, the covariance-based method developed by Yin and Cook (2002) for univariate regressions is ex-tended to multivariate response regressions and a new method is proposed. Simu-lated and real data examples illustrating the theory are presented. Key Words: Central k-th moment subspace, Central mean subspaces,
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